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If you still hear the motor sound, then chances are you need only a new mast. You can get one from most Corvette parts suppliers for about $29.95. The antenna can be removed easily from underneath the vehicle. Take it apart, put the new mast in and it should work. If no motor noise, then whole thing needs replacing, about$129.95. Job should take about 45 min. Good luck.
Yes. There are a couple of places to access the antenna power wire. One is under the passenger side knee bolster. Go the the Mid America web site, there is the instruction sheet for the antenna by-pass switch in the tech section. Print out the instructions and use the description to find the wire. Check it with a test light. In general, it is a pink wire on the big white connector in the wire bundle that runs to the rear of the car.
Some aftermarket radios do not have the wiring to use a power antenna. I would also check this out. You might be able to wire in a power switch for the antenna separately by gaining access to the power lead under the dash.